model 5 find new average from error Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Difference = 97 – 79 = 18

True average = 75 + $18/20$ = 75.9

Aliter : Using Rule 26,

If average of n numbers is m later on it was found that a number 'a’ was misread as 'b’.

The correct average will be = m +${\text"(a-b)"}/ \text"n"$.

Here, n = 20, m = 75

a = 97, b = 79

Correct mean = m + ${\text"(a - b)"}/\text"n"$

= 75 +${(97 -79)}/20$

= 75 +$18/20$

= 75 + 0.9 = 75.9

Answer: (d)

Total weight increased =$1/2$ × 50 = 25 kg.

∴ Weight of the new man = 50 + 25 = 75 kg.

Aliter : Using Rule 18,The age of the new person = T + N.t.

Here, N = 50, T = 50, t = $1/2$

Weight of New boy = T + Nt

= 50 + 50 × $1/2$ = 75 kg.

Answer: (d)

Required answer = 30 + 20 × 0.75

= 30 kg + 15 kg = 45 kg

Aliter : Using Rule 18,

If in the group of N persons, a new person comes at the place of a person of 'T’ years, so that average age,

increases by 't’ years

Then, the age of the new person = T + N.t.

Here, N = 20, T = 30, t = 0.75

Weight of New student = T + Nt

= 30 + 20 × 0.75

= 30 + 15 = 45 kg

Answer: (d)

Difference = 31 – 17 = 14

∴ Required average = 18 +$14/7$ = 20

Aliter : Using Rule 26,

If average of n numbers is m later on it was found that a number 'a’ was misread as 'b’.

The correct average will be = m +${\text"(a-b)"}/ \text"n"$.

Here, n = 7, m = 18

a = 31, b = 17

New Average = m + ${\text"(a - b)"}/\text"n"$

= 18 +${(31 – 17)}/7$

= 18 +$14/7$

= 18 + 2 = 20

Answer: (a)

Difference in observations

= 64 + 28 – 46 – 82 = – 36

∴ Correct average = 124 -$36/18$ = 122

Answer: (b)

Difference = 62 – 26 = 36

∴ Required average = 47 +$36/20$ = 47 + 1.8 = 48.8

Aliter : Using Rule 26,

The correct average will be = m +${\text"(a-b)"}/ \text"n"$.

Here, n = 20, m = 47

a = 62, b = 26

Correct Average = m + ${\text"(a - b)"}/\text"n"$

= 47 + ${(62 – 26)}/20$

= 47+$36/20$

= 47 + 1.8 = 48.8